Virendra and Gurindra purchased one camera each at the same prices. Later on Amrendra purchased both cameras at equal prices from Virendra and Gurindra. But the profit percentage of Virendra was P while the same of Gurindra was Q, since Gurindra calculated his profit on the selling price. Thus `Q=41 2/3%`Amrendra sells one of the camera to Dholakiya at `P%` profit, then what is die cost price for Dholakiya, while Amrendra purchased each of die camera at ₹ 240?

Options

A. ₹ 676
B. ₹ 500
C. ₹ 576
D. none

Answer

To solve the problem step by step, we will break down the information given and calculate the required values systematically.

### Step 1: Understand the Profit Percentage of Gurindra
Gurindra's profit percentage \( Q \) is given as \( 41 \frac{2}{3}\% \). This can be converted into an improper fraction:
\[ Q = \frac{125}{3}\% \]
This means that for every 100 units of selling price, Gurindra makes a profit of \( \frac{125}{3} \) units.

### Step 2: Calculate Selling Price and Cost Price for Gurindra
Since Gurindra calculates his profit based on the selling price, we can use the profit formula:
\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]
Let’s denote the cost price of the camera as \( CP \). The profit can be expressed as:
\[ \text{Profit} = \frac{Q}{100} \times SP \]
Given that \( Q = \frac{125}{3} \), we can express the selling price in terms of cost price:
\[ SP = CP + \frac{125}{300} \times SP \]
This simplifies to:
\[ SP - \frac{125}{300} \times SP = CP \]
\[ SP \left(1 - \frac{125}{300}\right) = CP \]
\[ SP \left(\frac{175}{300}\right) = CP \]
\[ SP = \frac{300}{175} \times CP = \frac{12}{7} \times CP \]

### Step 3: Determine Selling Price for Gurindra
Assuming \( CP = 240 \) (as both Virendra and Gurindra bought the cameras at the same price),
\[ SP = \frac{12}{7} \times 240 = 12 \times \frac{240}{7} = \frac{2880}{7} \approx 411.43 \]

### Step 4: Calculate Profit for Virendra
Since both cameras were bought at the same price, Virendra's selling price will also be \( SP = \frac{12}{7} \times CP \). The profit percentage \( P \) for Virendra can be calculated using the profit formula:
\[ P = \frac{\text{Profit}}{CP} \times 100 \]
Where profit is \( SP - CP \):
\[ P = \frac{\left(\frac{12}{7} \times 240 - 240\right)}{240} \times 100 \]
Calculating the profit:
\[ = \frac{\left(\frac{2880}{7} - 240\right)}{240} \times 100 \]
\[ = \frac{\left(\frac{2880 - 1680}{7}\right)}{240} \times 100 \]
\[ = \frac{\left(\frac{1200}{7}\right)}{240} \times 100 = \frac{1200 \times 100}{7 \times 240} \]
\[ = \frac{120000}{1680} \approx 71.43\% \]

### Step 5: Calculate Cost Price for Dholakiya
Amrendra sells one camera to Dholakiya at \( P\% \) profit. The cost price for Amrendra is \( 240 \):
\[ \text{Selling Price for Dholakiya} = CP + \left(\frac{P}{100} \times CP\right) \]
Substituting \( P \):
\[ = 240 + \left(\frac{71.43}{100} \times 240\right) \]
Calculating the selling price:
\[ = 240 + 171.43 \approx 411.43 \]

### Final Answer
Thus, the cost price for Dholakiya is approximately \( 411.43 \).